Cross-diffusion driven instability for a Lotka-Volterra competitive reaction-diffusion system

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Abstract

In this work we investigate the possibility of the pattern formation for areaction-di®usion system with nonlinear di®usion terms. Through a linear sta-bility analysis we ¯nd the conditions which allow a homogeneous steady state(stable for the kinetics) to become unstable through a Turing mechanism. Inparticular, we show how cross-di®usion e®ects are responsible for the initiationof spatial patterns. Finally, we ¯nd a Fisher amplitude equation which describesthe weakly nonlinear dynamics of the system near the marginal stability.
Original languageEnglish
Pages297-302
Number of pages6
Publication statusPublished - 2008

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